As a slow stopping apparatus for a working machine, there is known an apparatus for braking a motion speed of a boom at a constant acceleration to stop the working machine when a motion of the boom is stopped suddenly by an operating lever (for example, Patent Document 1). By reducing a speed at a constant acceleration, it is possible to slowly stop the boom, thereby suppressing a cargo swing.
However, the conventional slow stopping apparatus does not take a flexure of the boom into consideration. For this reason, there is a problem in that the boom is flexed in the stop of the motion of the boom and a cargo swing is caused by the flexure in a specific posture of the boom, particularly, a state in which the boom is extended.
On the other hand, Patent Document 2 discloses the technique for calculating a cargo swing cycle time in consideration of the flexure of the boom and braking a motion speed of the boom in a cargo swing cycle time at a constant acceleration, thereby carrying out stop. By the technique, it is possible to suppress a cargo swing including the flexure of the boom when stopping the motion of the boom.
It is known that an amount of the flexure of the boom is proportional to an acceleration and a mass (a weight) of a cargo supported by the boom. In more detail, the flexure of the boom can approximate to that of a cantilever and an amount δ of the flexure of the cantilever is expressed in the following Equation 1.
                    δ        =                              Fl            3                                3            ⁢                                                  ⁢            EI                                              [                  Equation          ⁢                                          ⁢          1                ]            wherein F represents a force to be applied in a perpendicular direction to a free end of a cantilever, I represents a length of the cantilever, E represents a Young's modulus of the cantilever, and I represents a secondary cross-sectional moment of the cantilever. In other words, the amount δ of the flexure is proportional to the force F to be applied to the cantilever. In the case of a flexure generated when the motion of the boom is stopped suddenly, the force F is an inertial force (F=ma) of the cargo supported on the boom. For this reason, the amount of the flexure of the boom is proportional to an acceleration a and a mass m of the cargo supported on the boom.
In the case in which the motion of the boom is stopped suddenly, the acceleration of the boom is increased with a rise in a motion speed just before a sudden stop, resulting in an increase in the acceleration of the cargo on the assumption that the motion speed is 0 within a constant time regardless of the motion speed of the boom. For this reason, the amount of the flexure of the boom is proportional to the motion speed just before a sudden stop. In other words, in the case in which the motion speed of the boom is high, the sudden stop causes the flexure of the boom to be increased, resulting in an increase in a load amplitude. On the other hand, in the case in which the motion speed of the boom is low, the sudden stop causes the amount of the flexure of the boom to be reduced, resulting in a decrease in the load amplitude. On the other hand, the cargo swing cycle time does not depend on the motion speed of the boom.
Referring to the technique described in the Patent Document 2, the cargo swing cycle time is taken to carry out stop regardless of the motion speed of the boom. For this reason, there is a problem in that a time required for the stop is increased also in the case in which the motion speed of the boom is low and the cargo swing does not matter.